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LCD Calculator

Write down the fractions separated by commas in the designated box, and the calculator will find their LCD (least common denominator), with detailed calculations shown.

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LCD (Least Common Denominator) Calculator

This free LCD calculator helps you find the least common denominator for any combination of fractions, making arithmetic operations on fractions easier and faster.

What is Least Common Denominator?

The smallest number that can serve as a common denominator for two or more fractions is called the LCD.

Essentially, the LCD is the least common multiple (LCM) of all denominators in a set of fractions. Our free calculator finds this instantly.

How to Find LCD of Integers, Fractions, or Mixed Numbers?

Convert all integers and mixed numbers into improper fractions.
Determine the least common denominator of all fractions.
Rewrite all fractions using the LCD as the denominator.

LCD Table

The following table shows LCDs for common fraction combinations:

Fractions	LCD
1/2, 1/4	4
1/2, 1/3	6
2/3, 5/9	9
2/3, 4/9, 5/6	18
2/3, 3/4, 4/5	60
2/3, 4/5	15
2/3, 1	3
2/3, 3/5, 4/7	105
2/3, 6/7	21
3/4, 6/7, 9/8	56
3/2, 5/4	4
3/4, 1/2	4
3/4, 5/6	12
4/5, 2/3, 5/7	105
4/5, 5/6, 7/15	30
4/3, 8/9, 3/5	45
5/6, 15/8	24
5/2, 8/9, 11/14	126
5/9, 4/15, 1/45	45
6/5, 8/25	25
6/8, 4/32	32
8/9, 10/27, 16/81	81
8/51, 19/85	255
9/2, 3, 9/4	4
9/14, 3/7	14

How to Find the Least Common Denominator Numerically?

Example #1: Find LCD for: 3, 1 2/3, 4/5, 5/8

Solution:

Convert to improper fractions: 3 = 3/1, 1 2/3 = 5/3
Denominators: 1, 3, 5, 8 → LCD = 120
Equivalent fractions:
- 3 = 360/120
- 1 2/3 = 200/120
- 4/5 = 96/120
- 5/8 = 75/120

Example #2: Find LCD for: 3/5, 6/3, 6/2, 3/9, 4

Solution:

Convert 4 → 4/1
Denominators: 5, 3, 2, 9, 1 → LCD = 90
Equivalent fractions:
- 3/5 = 54/90
- 6/3 = 180/90
- 6/2 = 270/90
- 3/9 = 30/90
- 4 = 360/90

How LCD Calculator Works

Input:

Enter integers, fractions, or mixed numbers separated by commas.
Click the Calculate button.

Output:

The least common denominator (LCD) of the fractions set.
Equivalent fractions expressed with the LCD.

FAQs

What is the LCD for 3/8, 9/2, and 8/5?

LCD = 40

What is the LCD for -2/7, 9/9, -4 7/3?

LCD = 63

Is there a difference between LCM and LCD?

Yes. LCD is a special case of LCM applied specifically to denominators of fractions.

What is a common numerator?

A number that is a multiple of all numerators in a set of fractions is called the common numerator.

How to compare fractions with unlike denominators?

Find their LCD first. Fractions with the same denominator can be compared by their numerators.

What is a common denominator for 9/7 and 2/7?

Since the denominators are the same, LCD = 7.

How to determine smaller or larger fractions with the same numerators?

The fraction with the larger denominator is smaller, and the fraction with the smaller denominator is larger.

What are unlike fractions?

Fractions with different denominators are called unlike fractions.

What is the smallest positive fraction?

1/6 (or 10/60 simplified) is an example.

Conclusion

Determining the LCD simplifies addition, subtraction, multiplication, and division of fractions. Our LCD calculator is a fast and reliable tool for fraction operations.

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